Where in your question does Perl come into play?

I think your question is mostly about jQuery, which is off-topic here. You should first check that sending the appropriate (hard-coded) JSON works. Then you can debug your Perl code until it creates the same JSON.

If you don't know what the correct JSON to create is, no fudging on the Perl side of the world will help you. You will need jQuery expertise, which certainly can be found. But this is not the forum for jQuery expertise.